Given x = -1 + 3i, y = -2 - 5i, find and simplify the following:

Question

 Given x = -1 + 3i, y = -2 - 5i, find and simplify the following:

a.      x + y

b.      xy

c.      x/y

d.     xy

Answer 1

x = -1 + 3i

y = -2 - 5i

x + y = (-1 + -2) + (3i + -5i) = -3 -2i

xy = (-1 + 3i)(-2 -5i) = (-1)(-2) + (-2)(3i) + (-5i)(-1) + (3i)(-5i) = 2 - 6i + 5i +15 = 17 - i

x/y = -1 + 3i * -2 + 5i = (-2 - 6i -5i - 15) = -17 - 11i

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-2 -5i -2 + 5i 4 + 25 29